1.⁠ ⁠HR se puuch ke batayenge: rivalq, magga, Kira_1234

 2.⁠ ⁠nulllösungssatz: Dominater069, aryanc403, IceKnight1093

 3.⁠ ⁠4C3: koderkushy, piyush_pransukhka, kingmessi

 4.⁠ ⁠tbd: keyurchd_11, shiven, GenghizKhan

 5.⁠ ⁠ElDiablo: ElDiablo

 6.⁠ ⁠rng: Atekichan, sv1shan

 7.⁠ ⁠SmolBrain: SmolBrain

 8.⁠ ⁠Pols_Station: Pols_Agyi_Pols

 9.⁠ ⁠PalindORme: the_hyp0cr1t3, JeevanJyot, ExplodingFreeze

10.⁠ ⁠Team: jtnydv25

11.⁠ ⁠Cult Council: AKSLEGION, D1orite, shorya1835

12.⁠ ⁠IDK: ha___il, JadeReaper, akcube

13.⁠ ⁠ThreeMusketeers: gakshat468, sg0071729, 21cs01033

14.⁠ ⁠cns_lena_chahiye_tha: dhruvsomani, vikram108, ParadigmShift

15.⁠ ⁠3CoOks: thirdcook, a_garg, Rayquaza

 1.⁠ ⁠ElDiablo: ElDiablo

 2.⁠ ⁠Team: jtnydv25

 3.⁠ ⁠monoid: htnaver, kayou81, atimanas

 4.⁠ ⁠No clue: Beelzebub_blue

 5.⁠ ⁠Death Valley: 1729_prism, Abhishek_821023, dark_ethics

We'll give prizes to the next 3 IITD teams not in the top 15.

A: ThreeMusketeers: gakshat468, sg0071729, 21cs01033

B: No clue: Beelzebub_blue

C: nulllösungssatz: Dominater069, aryanc403, IceKnight1093

D: HR se puuch ke batayenge: rivalq, magga, Kira_1234

E: nulllösungssatz: Dominater069, aryanc403, IceKnight1093

F: tbd: keyurchd_11, shiven, GenghizKhan

G: unforgettable playz: noobcodur, oviyan_gandhi, unforgettablepl

H: HR se puuch ke batayenge: rivalq, magga, Kira_1234

I: OverShadow: Coder_Nayak, Krypto_Ray, sloppy_coder

J: nulllösungssatz: Dominater069, aryanc403, IceKnight1093

K: nulllösungssatz: Dominater069, aryanc403, IceKnight1093

//solution to Highly Constrained Permutation

include<bits/stdc++.h>

using namespace std;

void solve() { int n; cin>>n; vector a(n+1),b(n+1);

for(int i=1;i<=n;i++) cin>>a[i];
for(int i=1;i<=n;i++) cin>>b[i];

vector<vector<int>> adj(n+1);

//make graph in the forward direction first
vector<int> last(n+1);
for(int i=1;i<=n;i++)
{
    //deal with last[a[i]-1] case
    if(a[i]!=1)
    {
        if(last[a[i]-1]==0)
        {
            cout<<-1<<'\n';
            return;
        }
        else adj[last[a[i]-1]].push_back(i);
    }
    //deal with the last[a[i]] case
    if(last[a[i]] != 0) adj[i].push_back(last[a[i]]);
    last[a[i]]=i;
}

//now in the backward direction
vector<int> next(n+1);
for(int i=n;i>=1;i--)
{
    //deal with next[b[i]-1] case
    if(b[i]!=1)
    {
        if(next[b[i]-1]==0)
        {
            cout<<-1<<'\n';
            return;
        }
        else  adj[i].push_back(next[b[i]-1]);
    }
    //deal with the next[b[i]] case
    if(next[b[i]] != 0) adj[next[b[i]]].push_back(i);
    next[b[i]]=i;
}

//so now toposort this graph
vector<bool> popped(n+1,false);
vector<int> indg(n+1);
queue<int> q;

// for(int i=1;i<=n;i++)
// {
//     cout<<i<<'\n';
//     for(auto j:adj[i]) cout<<j<<' ';
//     cout<<'\n';
// }

for(int i=1;i<=n;i++)
{
    for(auto j:adj[i]) indg[j]++;
}

for(int i=1;i<=n;i++)
{
    if(indg[i]==0) q.push(i);
}

vector<int> order;

while(!q.empty())
{
    int f=q.front();
    q.pop();
    popped[f]=true;
    order.push_back(f);

    for(auto nbr:adj[f]) 
    {
        indg[nbr]--;
        if(indg[nbr]==0) q.push(nbr);
    }
}

if((int)order.size() < n)
{
    printf("%d\n",-1);
    return;
}

vector<int> ans(n+1);
for(int i=0;i<n;i++) ans[order[i]]=i+1;

for(int i=1;i<=n;i++) printf("%d ",ans[i]);
printf("\n");

}

signed main() { int t; cin>>t; while(t--) solve(); }

include "bits/stdc++.h"

using namespace std;

int solve() { int n, x; cin >> n >> x;

const int msb = x >> 10 & 1;

if (msb == (n & 1)) return 10 * n;
return 10 * (n - 1) + 9;

}

int main() { cin.tie(nullptr)->sync_with_stdio(false);

int t;
cin >> t;
while (t--) cout << solve() << '\n';

}

include <bits/stdc++.h>

using namespace std;

define ll long long

ll rotate(ll x,ll base,vector & info){ if(x<base) return x; int k=0; for(int i=0;i<info.size();i++){ if(info[i]<=x&&info[i+1]>x){ k=i; break; } } return (info[k]*(x%base)+(x/base)); }

ll min_possible(ll x, ll base,vector & info){ if(x<base) return x; ll ans=x; for(int i=0;i<64;i++){ x=rotate(x,base,info); ans=min(ans,x); } return ans; }

void solve(vector <vector > & vect){ int n; cin >> n; ll sum=0; for(int i=0;i<n;i++){ ll x; cin>>x; sum+=min_possible(x,i+3,vect[i+3]); } cout<<sum<<endl; }

int main(){ int t; cin >> t; vector <vector > vect(1e5+3); for(int i=3;i<=1e5+2;i++){ ll cur=1; while(true){ vect[i].push_back(cur); if(cur>1e9) break; cur*=i; } } while(t--) solve(vect); }

include <bits/stdc++.h>

using namespace std;

int main() { long long int n,i,j; cin>>n; long long int marks[n+1]; int check[n+1]; for(i=1;i<=n;i++) { check[i]=0; } vector v; i=1; while(i<=n) { if(v.size()==0) { v.push_back(i); i++; } else { cout<<"? "<<v[v.size()-1]<<" "<<i<<endl; fflush(stdout); long long int x; cin>>x; marks[i]=abs(x); check[i]=1; if(x>0) { v.push_back(i); } else { v.pop_back(); } i++;

}
}
int honest_index=v[v.size()-1];
vector<pair<long long,long long>> first_half;
for(i=1;i<=n;i++)
{
    if(i!=honest_index)
    {
        if(check[i])
        {
            first_half.push_back({-marks[i],i});
        }
        else
        {
            cout<<"? "<<honest_index<<" "<<i<<endl;
            fflush(stdout);
            long long int dum;
            cin>>dum;
            marks[i]=abs(dum);
            check[i]=1;
            first_half.push_back({-marks[i],i});

        }
    }
}
sort(first_half.begin(),first_half.end());
int index=-1;
for(i=0;i<(n+1)/2;i++)
{
    int dum_indx=first_half[i].second;
    cout<<"? "<<honest_index<<" "<<dum_indx<<endl;
    fflush(stdout);
    long long int dum_marks;
    cin>>dum_marks;
    if(dum_marks>0)
    {
        index=dum_indx;
        marks[index]=dum_marks;
        break;
    }
}
cout<<"? "<<index<<" "<<honest_index<<endl;
fflush(stdout);
long long smth;
cin>>smth;
marks[honest_index]=smth;
if(marks[honest_index]>marks[index])
{

cout<<"! "<<honest_index<<endl;
}
else
{

cout<<"! "<<index<<endl;
}




return 0;

}

include "bits/stdc++.h"

include <ext/pb_ds/assoc_container.hpp>

include <ext/pb_ds/tree_policy.hpp>

using namespace std; using namespace __gnu_pbds;

define ordered_set tree<pair<int, int>, null_type, less<pair<int, int>>, rb_tree_tag, tree_order_statistics_node_update>

void solve(){

int n, q; cin >> n >> q;

vector<int> c(n);
for(int &x: c) cin >> x, x--;

vector<vector<int>> adj(n);
for(int i = 0; i < n-1; i++){
    int u, v; cin >> u >> v; 
    u--; v--;
    adj[u].push_back(v);
    adj[v].push_back(u);
}

ordered_set os[n];
vector<int> tin(n, 0), tout(n, 0);
int time = 0;

function<void(int, int)> dfs = [&](int v, int p){
    tin[v] = time++;
    for(int child: adj[v]){
        if(child != p) dfs(child, v);
    }
    tout[v] = time++;
    os[c[v]].insert({tin[v], v});
};

dfs(0, -1);

while(q--){

    int type, v, x; cin >> type >> v >> x;
    v--; x--;

    if(type == 1){
        os[c[v]].erase({tin[v], v});
        c[v] = x;
        os[c[v]].insert({tin[v], v});
    }
    else{
        auto firstit = os[x].order_of_key({tin[v], -1});
        auto lastit = os[x].order_of_key({tout[v], n+1});
        cout << lastit - firstit << '\n';
    }

}

}

signed main(){

ios::sync_with_stdio(0);
cin.tie(0);

int t = 1;
cin >> t;
while(t--) solve();

}

include <bits/stdc++.h>

using namespace std;

define endl '\n'

const int LOCATION = 4020; const int MAXP = 1001; const int SHIFT = 1010; long long dp[MAXP][LOCATION];

int main(){ ios::sync_with_stdio(0); cin.tie(0); int n, q; cin >> n >> q; vector a(n), p(n); for(int i = 0; i < n; i++){ cin >> a[i]; } for(int i = 0; i < n; i++){ cin >> p[i]; } for(int i = 0; i < n; i++){ dp[p[i]][a[i] + SHIFT] += 1ll; if(p[i] != 0) dp[p[i] — 1][a[i] + SHIFT] += 1ll; } for(int s = MAXP — 2; s >= 0; s--){ for(int i = 1; i < LOCATION — 1; i++){ dp[s][i] += dp[s + 1][i — 1] + dp[s + 1][i + 1] — (s + 2 < MAXP ? dp[s + 2][i] : 0); } } for(int i = 0; i < MAXP; i++){ for(int j = 1; j < LOCATION; j++){ dp[i][j] += dp[i][j — 1]; } } while(q--){ int l, r, s; cin >> l >> r >> s; l += SHIFT; r += SHIFT; cout << dp[s][r] — dp[s][l — 1] << endl; }

return 0;

}

include <bits/stdc++.h>

using namespace std;

define endl '\n'

bool solve(int s, int n, int k, int a[], int p[]){ vector<pair<int, int>> interval; for (int i = 0; i < n; i++) { if (p[i] — s >= 0) { int left = a[i] — p[i] + s; int right = a[i] + p[i] — s; interval.push_back({left, 1}); interval.push_back({right + 1, -1}); } } sort(interval.begin(), interval.end()); int m = 0, sm = 0; for (auto [_, v] : interval) { sm += v; m = max(m, sm); }

return m <= k;

}

int main(){ ios::sync_with_stdio(0); cin.tie(0); int t; cin >> t; while (t--) { int n, k; cin >> n >> k; int a[n], p[n]; for (int i = 0; i < n; i++) cin >> a[i]; for (int i = 0; i < n; i++) cin >> p[i]; int l = 0, r = 1e9 + 10; while (l <= r){ int mid = (l + r) / 2; if (solve(mid, n, k, a, p)) r = mid — 1; else l = mid + 1; } cout << l << endl; } }

include "bits/stdc++.h"

using namespace std;

define rep(i, a, b) for (auto i{a}; i < (b); ++i)

define per(i, a, b) for (auto i{b}; i-- > (a); )

define sz(x) (int)(x).size()

define all(x) (x).begin(), (x).end()

define rall(x) (x).rbegin(), (x).rend()

template bool uin(T& a, const T& b) { return a > b ? a = b, true : false; } template bool uax(T& a, const T& b) { return a < b ? a = b, true : false; }

using ll = long long; using poly = vector;

constexpr int mod = 998'244'353, root = 62;

int modpow(ll a, int b) { ll res = 1; for (; b; a = a * a % mod, b /= 2) if (b & 1) res = res * a % mod; return res; }

void ntt(poly &a) { int n = sz(a), L = 31 — __builtin_clz(n); static poly rt(2, 1); for (static int k = 2, s = 2; k < n; k *= 2, s++) { rt.resize(n); ll z[] = {1, modpow(root, mod >> s)}; rep(i,k,2*k) rt[i] = rt[i / 2] * z[i & 1] % mod; } vector rev(n); rep(i,0,n) rev[i] = (rev[i / 2] | (i & 1) << L) / 2; rep(i,0,n) if (i < rev[i]) swap(a[i], a[rev[i]]); for (int k = 1; k < n; k *= 2) for (int i = 0; i < n; i += 2 * k) rep(j,0,k) { ll z = rt[j + k] * a[i + j + k] % mod, &ai = a[i + j]; a[i + j + k] = ai — z + (z > ai ? mod : 0); ai += (ai + z >= mod ? z — mod : z); } } poly conv(const poly &a, const poly &b) { if (a.empty() || b.empty()) return {}; int s = sz(a) + sz(b) — 1, B = 32 — __builtin_clz(s), n = 1 << B; int inv = modpow(n, mod — 2); poly L(a), R(b), out(n); L.resize(n), R.resize(n); ntt(L), ntt(R); rep(i,0,n) out[-i & (n — 1)] = (ll)L[i] * R[i] % mod * inv % mod; ntt(out); return {out.begin(), out.begin() + s}; }

poly operator*(const poly& a, const poly& b) { return conv(a, b); }

constexpr int N = 2e5 + 10; ll fac[N];

ll mul(ll x, ll y) { return x * y % mod; }

int main() { cin.tie(nullptr)->sync_with_stdio(false);

fac[0] = 1;
rep(i, 1, N) fac[i] = mul(i, fac[i - 1]);

int n;
cin >> n;

vector<ll> a(n);
for (auto& x : a) cin >> x;

poly T(n);
for (int s = 1; s < n; ++s)
    T[s] = mul(fac[s - 1], fac[n - s - 1]);

vector<ll> score(n);

auto rec = [&](const auto& self, int l, int r, const poly& T) -> poly {
    if (r - l == 1) {
       poly P;
       if (l == n - 1) P = {0, 1};
       else P = {1, a[l + 1]};
       score[l] = (T[0] * P[0] + T[1] * P[1]) % mod;
       return P;
    }

    const int mid = l + (r - l) / 2;

    const poly Tr(T.begin(), T.begin() + (r - mid + 1));
    auto Pr = self(self, mid, r, Tr);

    reverse(all(Pr));
    auto Tl = Pr * T;
    Tl.erase(Tl.begin(), Tl.begin() + (r - mid));
    reverse(all(Pr));

    const auto Pl = self(self, l, mid, Tl);

    return Pl * Pr;
};
rec(rec, 1, n, T);

const auto to_div = modpow(fac[n - 1], mod - 2);
rep(i, 1, n) score[i] = mul(to_div, mul(i, mul(a[i], score[i])));

score[0] = 1;
for (auto x : a) score[0] = mul(score[0], x);

rep(i, 0, n) cout << score[i] << " \n"[i == n - 1];

}

include<bits/stdc++.h>

using namespace std;

void solve() { int n, k, m; cin >> n >> k >> m; vector v(n); for (int i = 0; i < n; i++) { cin >> v[i]; } vector<pair<int, int>> q(m); for (int i = 0; i < m; i++) { cin >> q[i].first >> q[i].second; } vector ans(m); auto calc = & { vector<vector> suf(n + 1, vector(k + 1)); for (int i = n — 1; i >= 0; i--) { suf[i] = suf[i + 1]; int cost = 0, sum = 0; for (int j = i; j < n; j++) { cost += (v[j] > 0); sum -= abs(v[j]); if (cost <= k) { suf[i][cost] = min(suf[i][cost], sum); } } for (int j = 1; j <= k; j++) { suf[i][j] = min(suf[i][j], suf[i][j — 1]); } } vector dp(n + 1, 1); vector h(n + 1, k + 1); h[0] = 0; for (int i = 0; i <= n; i++) { if (i > 0) { int cost = 0, sum = 0; for (int j = i — 1; j >= 0; j--) { cost += (v[j] < 0); sum += abs(v[j]); h[sum] = min(h[sum], cost); } } for (int j = 0; j <= n; j++) { if (h[j] <= k) { dp[j] = min(dp[j], suf[i][k — h[j]]); } } } for (int i = 0; i < m; i++){ for (int j = 0; j <= n; j++){ if (dp[j] <= 0){ ans[i] = max(ans[i], q[i].first * j — q[i].second * dp[j]); } } } }; calc(); reverse(v.begin(), v.end()); calc(); for (int i = 0; i < m; i++){ cout << ans[i] << " \n"[i == m — 1]; } }

int main() { ios::sync_with_stdio(0); cin.tie(0); int t; cin >> t; while (t--) { solve(); } return 0; }

include<bits/stdc++.h>

define int long long

using namespace std;

const int N=1e6+100; const int mod = 1e9+7; vector fact(N+1); vector ifact(N+1);

int binexp(int a,int n) { if(n==0) return 1; else { int res=binexp(a,n/2); res=(res*res)%mod; if(n&1) res=(res*a)%mod; return res; } }

int ncr(int n,int r) { if(r>n || r<0 || n<0) return 0; int ans=(fact[n]*ifact[r])%mod; ans=(ans*ifact[n-r])%mod; return ans; }

void solve() { int n,x,y; cin>>n>>x>>y; int dif=abs(x-y); cout<<ncr(n-2,dif-1)<<'\n'; }

signed main() { int t; cin>>t;

fact[0]=1;
for(int i=1;i<=N;i++) fact[i]=(fact[i-1]*i)%mod;
ifact[N]=binexp(fact[N],mod-2);
for(int i=N-1;i>=0;i--) ifact[i]=(ifact[i+1]*(i+1))%mod;

while(t--) solve();

}

include "bits/stdc++.h"

using namespace std;

define rep(i, a, b) for (auto i{a}; i < (b); ++i)

define per(i, a, b) for (auto i{b}; i-- > (a); )

define sz(x) (int)(x).size()

define all(x) (x).begin(), (x).end()

define rall(x) (x).rbegin(), (x).rend()

template bool uin(T& a, const T& b) { return a > b ? a = b, true : false; } template bool uax(T& a, const T& b) { return a < b ? a = b, true : false; }

using ll = long long;

using U = uint32_t; using poly = vector;

constexpr int mod = 998'244'353, root = 62;

int modpow(ll a, int b) { ll res = 1; for (; b; a = a * a % mod, b /= 2) if (b & 1) res = res * a % mod; return res; }

void ntt(poly &a) { int n = sz(a), L = 31 — __builtin_clz(n); static poly rt(2, 1); for (static int k = 2, s = 2; k < n; k *= 2, s++) { rt.resize(n); ll z[] = {1, modpow(root, mod >> s)}; rep(i,k,2*k) rt[i] = rt[i / 2] * z[i & 1] % mod; } vector rev(n); rep(i,0,n) rev[i] = (rev[i / 2] | (i & 1) << L) / 2; rep(i,0,n) if (i < rev[i]) swap(a[i], a[rev[i]]); for (int k = 1; k < n; k *= 2) for (int i = 0; i < n; i += 2 * k) rep(j,0,k) { ll z = rt[j + k] * a[i + j + k] % mod, &ai = a[i + j]; a[i + j + k] = ai — z + (z > ai ? mod : 0); ai += (ai + z >= mod ? z — mod : z); } } poly conv(const poly &a, const poly &b) { if (a.empty() || b.empty()) return {}; int s = sz(a) + sz(b) — 1, B = 32 — __builtin_clz(s), n = 1 << B; int inv = modpow(n, mod — 2); poly L(a), R(b), out(n); L.resize(n), R.resize(n); ntt(L), ntt(R); rep(i,0,n) out[-i & (n — 1)] = (ll)L[i] * R[i] % mod * inv % mod; ntt(out); return {out.begin(), out.begin() + s}; }

constexpr int N = 1e5;

ll mul(ll x, ll y) { return x * y % mod; }

int fac[N], ifac[N]; int C(int n, int r) { return mul(fac[n], mul(ifac[r], ifac[n — r])); }

int solve() { int n, m, k; cin >> n >> m >> k;

vector<vector<int>> g(k);
rep(e, 0, m) {
    char a, b;
    cin >> a >> b;
    const int u = a - 'a', v = b - 'a';
    g[u].push_back(v);
    g[v].push_back(u);
}

vector Q(k + 1, poly(n + 1, 0));
for (int t = 1; t <= k; ++t)
    for (int r = t; r <= n; ++r)
       Q[t][r] = mul(ifac[r], C(r - 1, t - 1));

auto merge = [&](const poly& a, const poly& b) {
    auto c = conv(a, b);
    c.resize(n + 1, 0);
    return c;
};

ll res = 0;
vector<poly> f(1 << k);
f[0].assign(n + 1, 0);
f[0][0] = 1;
rep(S, 1u, 1u << k) {
    const auto root = 31 ^ __builtin_clz(S);
    assert(S >> root & 1);

    U T = 0;
    {
       auto dfs = [&](const auto& self, int u) -> void {
         T |= 1u << u;
         for (auto v : g[u])
          if ((~T & S) >> v & 1)
              self(self, v);
       };
       dfs(dfs, root);
    }

    const int t = popcount(T);
    f[S] = merge(f[S ^ T], Q[t]);
    res += f[S][n];
}
return mul(res % mod, fac[n]);

}

int main() { cin.tie(nullptr)->sync_with_stdio(false);

fac[0] = 1;
rep(i, 1, N) fac[i] = mul(i, fac[i - 1]);
ifac[N - 1] = modpow(fac[N - 1], mod - 2);
per(i, 1, N) ifac[i - 1] = mul(i, ifac[i]);

int t;
cin >> t;
while (t--) cout << solve() << '\n';

}